Question

Solve this system of linear equations. Separate

the x. and y-values with a comma.
- 7x + 3y = 22
4x + 2y = 10

Answer 1

`(-(7)/(13),(79)/(13))`

Explanation:

Given:

Two equations are given.

`- 7x + 3y = 22`------(1)

`4x + 2y = 10`----------(2)

Solve equation 1 for y.

`- 7x + 3y = 22`

`3y = 22+7x`

`y=(22+7x)/(3)`-----------(3)

Now, we substitute y value in equation 2.

`4x + 2((22+7x)/(3)) = 10`

`(12x + 2(22+7x))/(3) = 10`

`12x + 2(22+7x)=10* 3`

`12x + 44+14x=30`

`26x=30-44`

`26x=-14`

`x=-(14)/(26)`

`x=-(7)/(13)`

Now, we substitute x value in equation 1.

`- 7(-(7)/(13)) + 3y = 22`

`(7* 7)/(13) + 3y = 22`

`(49)/(13) + 3y = 22`

`3y = 22-(49)/(13)`

`3y = (13* 22-49)/(13)`

`3y = (286-49)/(13)`

`y = (237)/(13* 3)`

`y = (237)/(39)`

`y = (79)/(13)`

Therefore, the value of x and y is
`(x=-(7)/(13),y = (79)/(13))`